By effectively utilizing the fidelity of a physical simulation and the flexibility of a numerical simulation, the hybrid simulation is applicable to test the complicated docking contact process of various kinds of spacecraft. However, the hybrid simulation of space docking often has a divergence or convergence distortion due to phase delays and structure dynamics in the system loops. In many cases, it is difficult to derive the loop models based on the first-principle for the compensator design. In this study, a learning-based distortion compensation method is proposed to compensate for the phase delays and structure dynamics existing in the simulator. The measurement system delay of the contact force is compensated by a learning-based force compensator (LFC). For the motion simulator, the delay of the actuation system of the lower platform is compensated by a learning-based actuation compensator (LAC), and the structure dynamics of the lower and upper platforms are compensated by a learning-based structure compensator (LSC). The proposed learning-based distortion compensation method does not require the system models. Some verifications show that the hybrid simulation error can be reduced and good accuracy can be achieved.